Nintendo's nearly-as-popular successor to the Game Boy, with graphics comparable to the SNES. There were three very different hardware versions released, each with distinct advantages and disadvantages. It can link up to the Nintendo GameCube as a secondary display, and there are actually quite a few games that utilized this heavily. GBA games will play on the Gamecube (via the Game Boy Player peripheral) DS and DS Lite, but not the DSi.
There is a bulky add-on called the E-Reader, which could load data off (something like) bar codes. It's used to transmit Animal Crossing items from cards, play NES ports (that have to be loaded from multiple cards), and bonus Super Mario Bros. 3 levels. Nothing original other than a few minigames ever came out for it.
Ebay is plagued by GBA cartridge piracy. If it's unboxed (especially if they offer to send the box flattened/unmade), and sounds too-cheap-to-be-true, avoid it. They tend to have poor batteries that won't keep your save data for long.
The Famicom Mini series is a line of 30 Famicom, and Famicom Disk System, ports released to commemorate the Famicom's 20th anniversary. A similar, smaller, series was released outside Japan (as the Classic NES Series in North America, and NES Classics in PAL territories), but their ports are based on the NES releases. So no FDS Metroid, and Kid Icarus.
A few of the FDS ports are worth picking up, mostly for the better sound, no disk-swapping or load times, and the use of on-cart saves, instead of passwords.